The development of an eBook for teaching and learning mathematics

Mobile devices, smartphones, phablets and tablets, are widely avail‐ able. This is a generation of digital natives. We cannot ignore that they are no longer the same students for which the education system was designed tradition‐ ally. Studying math is many times a cumbersome task. But this can be changed if the teacher takes advantage of the technology that is currently available. We are working in the use of different tools to extend the classroom in a blended learning model. In this paper, it is presented the development of an eBook for teaching mathematics to secondary students. It is developed with the free and open standard EPUB 3 that is available for Android and iOS platforms. This specification supports video embedded in the eBook. In this paper it is shown how to take advantage of this feature, making videos available about lectures and problems resolutions, which is especially interesting for learning mathematics.

A model eliciting framework for integrating mathematics and robotics learning

Robotics is taught in many Australian ICT classrooms, in both primary and secondary schools. Robotics activities, including those developed using the LEGO Mindstorms NXT technology, are mathematics-rich and provide a fertile round for learners to develop and extend their mathematical thinking. However, this context for learning mathematics is often under-exploited. In this paper a variant of the model construction sequence (Lesh, Cramer, Doerr, Post, & Zawojewski, 2003) is proposed, with the purpose of explicitly integrating robotics and mathematics teaching and learning. Lesh et al.’s model construction sequence and the model eliciting activities it embeds were initially researched in primary mathematics classrooms and more recently in university engineering courses. The model construction sequence involves learners working collaboratively upon product-focussed tasks, through which they develop and expose their conceptual understanding. The integrating model proposed in this paper has been used to design and analyse a sequence of activities in an Australian Year 4 classroom. In that sequence more traditional classroom learning was complemented by the programming of LEGO-based robots to ‘act out’ the addition and subtraction of simple fractions (tenths) on a number-line. The framework was found to be useful for planning the sequence of learning and, more importantly, provided the participating teacher with the ability to critically reflect upon robotics technology as a tool to scaffold the learning of mathematics.

Grupo de estudos de professores e a produção de atividades matemáticas sobre funções utilizando computadores

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Dois jogos de linguagem: a informática e a matemática na aprendizagem de função quadrática

Esta pesquisa foi realizada com o objetivo de identificar e analisar as relações entre as linguagens da Matemática e da Informática no contexto da sala de aula, a partir da inserção das tecnologias informáticas na aprendizagem da Função Quadrática. Nesse sentido, os conceitos que envolvem a forma algébrica e forma gráfica desta função, foram observados pelos alunos ao explorar aspectos dinâmicos na interface do Geogebra. A fundamentação teórica da pesquisa, foi subsidiada pelas ideias de Pierre Lévy sobre as tecnologias da inteligência na disseminação da informação e do conhecimento, bem como pelas contribuições filosóficas de Ludwig Wittgenstein acerca do jogo de linguagem. A metodologia da pesquisa possui caráter qualitativo definido a partir de critérios específicos acerca do objeto de estudo e dos sujeitos investigados. As informações foram obtidas por meio de questões específicas aplicadas em dois momentos, a saber: antes e após a realização de um minicurso sobre o GeoGebra. As análises das questões revelaram que os aspectos visuais e os movimentos no uso do computador, estabelecem relações entre as formas algébricas e gráficas da função quadrática. Assim, eles puderam perceber que os coeficientes numéricos modificam a parábola e isso dá sentido aos conceitos estudados. O uso do GeoGebra possibilita outras formas de aprendizagem evidenciadas entre o Jogo de Linguagem da Matemática e o Jogo de Linguagem da Informática no âmbito da Educação Matemática.

Problemas de máximos e mínimos no Ensino Médio

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Reading as a Learning Strategy for Mathematics

In this action research study of 55 sophomore and junior students in my Algebra II/Trigonometry classrooms, I investigated a reading strategy of learning mathematics. Students were given background information about reading and explored the benefits of reading for themselves. Next, students were taught to read their textbook, analyzing one section of the textbook at a time. Throughout the research project, students were given reading guides to fill out during class with whole class discussion following the reading time. I discovered that students are able to read a mathematics textbook with understanding and students who are gone for activities can learn independently. Teacher observations, student surveys, and student interviews provide quantitative evidence of increased student understanding and achievement. As a result of this research, I plan to continue utilizing the reading guides and incorporating reading as a method of learning mathematics within my classrooms.

Motivation and Learning in Mathematics Pre-service Teachers

Based on a review of literature of conceptual and procedural knowledge in relation to intrinsic and extrinsic motivation, the purpose of this study was to test the relationship between conceptual and procedural knowledge and intrinsic and extrinsic motivation. Thirty-eight education students with a mathematics focus (elementary or secondary) in their junior, senior, or fifth year completed a survey with a Likert scale measuring their preference to learning (conceptual or procedural) and their motivation type (intrinsic or extrinsic). Findings showed that secondary mathematics focused students were more likely to prefer learning mathematics conceptually than elementary mathematics focused students. However, secondary and elementary mathematics focused students showed an equal preference for learning mathematics procedurally and sequentially. Elementary and secondary students reported similar intrinsic and extrinsic motivation. Extrinsically motivated students preferred procedural learning more than conceptual learning. While there was no statistically significant preference with intrinsically motivated students, there was a trend favoring preference of conceptual learning over procedural learning. These results tend to support the hypothesis that mathematics focused students who prefer conceptual learning are more intrinsically motivated, and mathematics focused students who prefer procedural learning are more extrinsically motivated.

Understanding Teacher and Student Learning Situated in a School-wide Implementation of Fractions Instruction

Thesis (Ph.D.)--University of Washington, 2016-06

A utilização de softwares no ensino de funções quadráticas

Este projeto tem como objetivo apresentar uma maneira diferente de abordar os conceitos de funções quadráticas, propondo exercícios de motivação e de fixação de conteúdos, com questões contextualizadas e voltadas para o dia-a-dia do educando. Pretende-se auxiliar os docentes e tornar, assim, a aprendizagem de seus discentes mais prazerosa, desmistificando a Matemática, oportunizando aos alunos a utilização dos conceitos matemáticos em seu cotidiano. Utilizando as ferramentas tecnológicas já disponíveis na maioria das escolas de Educação Básica, apresentarse-ão atividades usando pelo menos um software livre para inspirar os professores na elaboração de suas aulas e consequentemente ajudar os discentes na construção do seu conhecimento.

Investigating problem-based learning in Saudi Arabian mathematics education: a TIMSS-related study

The aim of this study is to investigate the effectiveness of problem-based learning (PBL) on students’ mathematical performance. This includes mathematics achievement and students’ attitudes towards mathematics for third and eighth grade students in Saudi Arabia. Mathematics achievement includes, knowing, applying, and reasoning domains, while students’ attitudes towards mathematics covers, ‘Like learning mathematics���, ‘value mathematics���, and ‘a confidence to learn mathematics���. This study goes deeper to examine the interaction of a PBL teaching strategy, with trained face-to-face and self-directed learning teachers, on students’ performance (mathematics achievement and attitudes towards mathematics). It also examines the interaction between different ability levels of students (high and low levels) with a PBL teaching strategy (with trained face-to-face or self-directed learning teachers) on students’ performance. It draws upon findings and techniques of the TIMSS international benchmarking studies. Mixed methods are used to analyse the quasi-experimental study data. One -way ANOVA, Mixed ANOVA, and paired t-tests models are used to analyse quantitative data, while a semi-structured interview with teachers, and author’s observations are used to enrich understanding of PBL and mathematical performance. The findings show that the PBL teaching strategy significantly improves students’ knowledge application, and is better than the traditional teaching methods among third grade students. This improvement, however, occurred only with the trained face-to-face teacher’s group. Furthermore, there is robust evidence that using a PBL teaching strategy could raise significantly students’ liking of learning mathematics, and confidence to learn mathematics, more than traditional teaching methods among third grade students. Howe ver, there was no evidence that PBL could improve students’ performance (mathematics achievement and attitudes towards mathematics), more than traditional teaching methods, among eighth grade students. In 8th grade, the findings for low achieving students show significant improvement compared to high achieving students, whether PBL is applied or not. However, for 3th grade students, no significant difference in mathematical achievement between high and low achieving students was found. The results were not expected for high achieving students and this is also discussed. The implications of these findings for mathematics education in Saudi Arabia are considered.

e-Math Workshops : a forum for exchanging experiences of mathematics e-learning at university level

We report here about a series of international workshops on e-learning of mathematics at university level, which have been jointly organized by the three publicly funded open universities in the Iberian Peninsula and which have taken place annually since 2009. The history, achievements and prospects for the future of this initiative will be addressed.

Integrating concrete and virtual materials in an elementary mathematics classroom : a case study of success with fractions

This paper describes an approach to introducing fraction concepts using generic software tools such as Microsoft Office's PowerPoint to create "virtual" materials for mathematics teaching and learning. This approach replicates existing concrete materials and integrates virtual materials with current non-computer methods of teaching primary students about fractions. The paper reports a case study of a 12-year-old student, Frank, who had an extremely limited understanding of fractions. Frank also lacked motivation for learning mathematics in general and interacted with his peers in a negative way during mathematics lessons. In just one classroom session involving the seamless integration of off-computer and on-computer activities, Frank acquired a basic understanding of simple common equivalent fractions. Further, he was observed as the session progressed to be an enthusiastic learner who offered to share his learning with his peers. The study's "virtual replication" approach for fractions involves the manipulation of concrete materials (folding paper regions) alongside the manipulation of their virtual equivalent (shading screen regions). As researchers have pointed out, the emergence of new technologies does not mean old technologies become redundant. Learning technologies have not replaced print and oral language or basic mathematical understanding. Instead, they are modifying, reshaping, and blending the ways in which humankind speaks, reads, writes, and works mathematically. Constructivist theories of learning and teaching argue that mathematics understanding is developed from concrete to pictorial to abstract and that, ultimately, mathematics learning and teaching is about refinement and expression of ideas and concepts. Therefore, by seamlessly integrating the use of concrete materials and virtual materials generated by computer software applications, an opportunity arises to enhance the teaching and learning value of both materials.